Question

For a moving object, the force acting on the object varles directly with the object's acceleration. When a force of 30 N acts on a certain object, the accelerationof the object is 3 m/s?. If the force is changed to 80 N, what will be the acceleration of the object?

Answer 1

Step-by-step explanation:

Let Force = F

Acceleration = A

`\begin{gathered} \text{Force varies directly with object's acceleration} \\ \text{Mathematically:} \\ F\text{ }\alpha\text{ A} \\ F\text{ = }kA \\ \text{where k = constant of proportionality} \end{gathered}`

when Force = 30N, accelration = 3m/s

We will susbtitute the values above in the equation to get k:

`\begin{gathered} 30\text{ = k(3)} \\ 30\text{ = 3k (divide both sides by 3)} \\ k\text{ = 30/3} \\ k\text{ = 10} \end{gathered}`

The equation showing the relationship between force and acceleration becomes:

`F\text{ = 10A}`

when Force = 80N

accelration = ?

To get acceleration, we will substitute in the formula relating the variables: